How to prove every model is the bounded morphic image of the disjoint union of point-generated models？ [on...
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When doing the exercises in Blackburn’s modal logic，I have been puzzled by a question in Chapter 2.1.
The question is: How to prove every model is the bounded morphic image of the disjoint union of point-generated models？
As hinted in the book, the proof is quite straightforward, however, I even don't know how to prove one model is the bounded morphic image of another. I know the definition but how could I find the function f?
logic model-theory
asked 2 days ago
Coco LeeCoco Lee
11
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Coco Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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put on hold as off-topic by amWhy, Lord_Farin, José Carlos Santos, Yanko, metamorphy 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord_Farin, José Carlos Santos, Yanko, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
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When doing the exercises in Blackburn’s modal logic，I have been puzzled by a question in Chapter 2.1.
The question is: How to prove every model is the bounded morphic image of the disjoint union of point-generated models？
As hinted in the book, the proof is quite straightforward, however, I even don't know how to prove one model is the bounded morphic image of another. I know the definition but how could I find the function f?
logic model-theory
asked 2 days ago
Coco LeeCoco Lee
11
New contributor
Coco Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by amWhy, Lord_Farin, José Carlos Santos, Yanko, metamorphy 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord_Farin, José Carlos Santos, Yanko, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
I would guess that for each element (each 'possible world') $a$ of the model $W$ you take a new copy $W_a'$ of the point-generated submodel $W_a$. Then you can map the disjoint union $bigcup_a W_a'$ onto $W$ by mapping each $W_a'$ isomorphically back onto $W_a$.
– realdonaldtrump
2 days ago
2
If you're wondering why the question was put on hold, it's probably because you didn't include enough context - you should always include the relevant definitions, unless they're very standard. The word "model" has different meanings in different contexts. Here I guess you mean a model in the sense of modal logic, i.e. a frame with valuations of the proposition symbols? What is a bounded morphic image? What does it mean for a model to be point-generated? And by the way, I believe your book is called "Modal Logic", not "Model Logic".
– Alex Kruckman
2 days ago
And welcome to math stackexchange. Here are some tips on how to ask good questions: math.meta.stackexchange.com/questions/9959/…
– Alex Kruckman
2 days ago
add a comment |
0
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When doing the exercises in Blackburn’s modal logic，I have been puzzled by a question in Chapter 2.1.
The question is: How to prove every model is the bounded morphic image of the disjoint union of point-generated models？
As hinted in the book, the proof is quite straightforward, however, I even don't know how to prove one model is the bounded morphic image of another. I know the definition but how could I find the function f?
logic model-theory
asked 2 days ago
Coco LeeCoco Lee
11
New contributor
Coco Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
When doing the exercises in Blackburn’s modal logic，I have been puzzled by a question in Chapter 2.1.
The question is: How to prove every model is the bounded morphic image of the disjoint union of point-generated models？
As hinted in the book, the proof is quite straightforward, however, I even don't know how to prove one model is the bounded morphic image of another. I know the definition but how could I find the function f?
logic model-theory
logic model-theory
asked 2 days ago
Coco LeeCoco Lee
11
New contributor
Coco Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Coco LeeCoco Lee
11
New contributor
Coco Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Coco Lee
asked 2 days ago
Coco LeeCoco Lee
11
New contributor
Coco Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Coco LeeCoco Lee
11
asked 2 days ago
Coco LeeCoco Lee
11
11
New contributor
Coco Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Coco Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Coco Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by amWhy, Lord_Farin, José Carlos Santos, Yanko, metamorphy 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord_Farin, José Carlos Santos, Yanko, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by amWhy, Lord_Farin, José Carlos Santos, Yanko, metamorphy 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lord_Farin, José Carlos Santos, Yanko, metamorphy
If this question can be reworded to fit the rules in the help center, please edit the question.
I would guess that for each element (each 'possible world') $a$ of the model $W$ you take a new copy $W_a'$ of the point-generated submodel $W_a$. Then you can map the disjoint union $bigcup_a W_a'$ onto $W$ by mapping each $W_a'$ isomorphically back onto $W_a$.
– realdonaldtrump
2 days ago
2
If you're wondering why the question was put on hold, it's probably because you didn't include enough context - you should always include the relevant definitions, unless they're very standard. The word "model" has different meanings in different contexts. Here I guess you mean a model in the sense of modal logic, i.e. a frame with valuations of the proposition symbols? What is a bounded morphic image? What does it mean for a model to be point-generated? And by the way, I believe your book is called "Modal Logic", not "Model Logic".
– Alex Kruckman
2 days ago
And welcome to math stackexchange. Here are some tips on how to ask good questions: math.meta.stackexchange.com/questions/9959/…
– Alex Kruckman
2 days ago
add a comment |
I would guess that for each element (each 'possible world') $a$ of the model $W$ you take a new copy $W_a'$ of the point-generated submodel $W_a$. Then you can map the disjoint union $bigcup_a W_a'$ onto $W$ by mapping each $W_a'$ isomorphically back onto $W_a$.
– realdonaldtrump
2 days ago
2
If you're wondering why the question was put on hold, it's probably because you didn't include enough context - you should always include the relevant definitions, unless they're very standard. The word "model" has different meanings in different contexts. Here I guess you mean a model in the sense of modal logic, i.e. a frame with valuations of the proposition symbols? What is a bounded morphic image? What does it mean for a model to be point-generated? And by the way, I believe your book is called "Modal Logic", not "Model Logic".
– Alex Kruckman
2 days ago
And welcome to math stackexchange. Here are some tips on how to ask good questions: math.meta.stackexchange.com/questions/9959/…
– Alex Kruckman
2 days ago
I would guess that for each element (each 'possible world') $a$ of the model $W$ you take a new copy $W_a'$ of the point-generated submodel $W_a$. Then you can map the disjoint union $bigcup_a W_a'$ onto $W$ by mapping each $W_a'$ isomorphically back onto $W_a$.
– realdonaldtrump
2 days ago
I would guess that for each element (each 'possible world') $a$ of the model $W$ you take a new copy $W_a'$ of the point-generated submodel $W_a$. Then you can map the disjoint union $bigcup_a W_a'$ onto $W$ by mapping each $W_a'$ isomorphically back onto $W_a$.
– realdonaldtrump
2 days ago
2
2
If you're wondering why the question was put on hold, it's probably because you didn't include enough context - you should always include the relevant definitions, unless they're very standard. The word "model" has different meanings in different contexts. Here I guess you mean a model in the sense of modal logic, i.e. a frame with valuations of the proposition symbols? What is a bounded morphic image? What does it mean for a model to be point-generated? And by the way, I believe your book is called "Modal Logic", not "Model Logic".
– Alex Kruckman
2 days ago
If you're wondering why the question was put on hold, it's probably because you didn't include enough context - you should always include the relevant definitions, unless they're very standard. The word "model" has different meanings in different contexts. Here I guess you mean a model in the sense of modal logic, i.e. a frame with valuations of the proposition symbols? What is a bounded morphic image? What does it mean for a model to be point-generated? And by the way, I believe your book is called "Modal Logic", not "Model Logic".
– Alex Kruckman
2 days ago
And welcome to math stackexchange. Here are some tips on how to ask good questions: math.meta.stackexchange.com/questions/9959/…
– Alex Kruckman
2 days ago
And welcome to math stackexchange. Here are some tips on how to ask good questions: math.meta.stackexchange.com/questions/9959/…
– Alex Kruckman
2 days ago
add a comment |
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I would guess that for each element (each 'possible world') $a$ of the model $W$ you take a new copy $W_a'$ of the point-generated submodel $W_a$. Then you can map the disjoint union $bigcup_a W_a'$ onto $W$ by mapping each $W_a'$ isomorphically back onto $W_a$.
– realdonaldtrump
2 days ago
2
If you're wondering why the question was put on hold, it's probably because you didn't include enough context - you should always include the relevant definitions, unless they're very standard. The word "model" has different meanings in different contexts. Here I guess you mean a model in the sense of modal logic, i.e. a frame with valuations of the proposition symbols? What is a bounded morphic image? What does it mean for a model to be point-generated? And by the way, I believe your book is called "Modal Logic", not "Model Logic".
– Alex Kruckman
2 days ago
And welcome to math stackexchange. Here are some tips on how to ask good questions: math.meta.stackexchange.com/questions/9959/…
– Alex Kruckman
2 days ago