Is any cross-fertilization occurring between the disciplines of game semantics and set theory?
I've recently been introduced (at a superficial 'wiki' level) to the Axiom of determinacy and Descriptive set theory.
While looking up Witness_(mathematics), I found the link to Game semantics.
Are researchers in these two disciplines, set theory and game
semantics, able to 'jam together'?
Please excuse the vagueness of this soft question. But what can you expect from a wiki-dabbler?
Just hoping it can generate some interesting comments/answers so I can learn something...
logic soft-question set-theory
asked Dec 4 '18 at 20:46
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4,0651627
add a comment |
I've recently been introduced (at a superficial 'wiki' level) to the Axiom of determinacy and Descriptive set theory.
While looking up Witness_(mathematics), I found the link to Game semantics.
Are researchers in these two disciplines, set theory and game
semantics, able to 'jam together'?
Please excuse the vagueness of this soft question. But what can you expect from a wiki-dabbler?
Just hoping it can generate some interesting comments/answers so I can learn something...
logic soft-question set-theory
asked Dec 4 '18 at 20:46
CopyPasteItCopyPasteIt
4,0651627
1
plato.stanford.edu/entries/logic-games (and jelly not jam)
– Not Mike
Dec 5 '18 at 7:44
add a comment |
I've recently been introduced (at a superficial 'wiki' level) to the Axiom of determinacy and Descriptive set theory.
While looking up Witness_(mathematics), I found the link to Game semantics.
Are researchers in these two disciplines, set theory and game
semantics, able to 'jam together'?
Please excuse the vagueness of this soft question. But what can you expect from a wiki-dabbler?
Just hoping it can generate some interesting comments/answers so I can learn something...
logic soft-question set-theory
asked Dec 4 '18 at 20:46
CopyPasteItCopyPasteIt
4,0651627
I've recently been introduced (at a superficial 'wiki' level) to the Axiom of determinacy and Descriptive set theory.
While looking up Witness_(mathematics), I found the link to Game semantics.
Are researchers in these two disciplines, set theory and game
semantics, able to 'jam together'?
Please excuse the vagueness of this soft question. But what can you expect from a wiki-dabbler?
Just hoping it can generate some interesting comments/answers so I can learn something...
logic soft-question set-theory
logic soft-question set-theory
asked Dec 4 '18 at 20:46
CopyPasteItCopyPasteIt
4,0651627
asked Dec 4 '18 at 20:46
CopyPasteItCopyPasteIt
4,0651627
asked Dec 4 '18 at 20:46
CopyPasteItCopyPasteIt
4,0651627
asked Dec 4 '18 at 20:46
CopyPasteItCopyPasteIt
4,0651627
asked Dec 4 '18 at 20:46
CopyPasteItCopyPasteIt
4,0651627
4,0651627
1
plato.stanford.edu/entries/logic-games (and jelly not jam)
– Not Mike
Dec 5 '18 at 7:44
add a comment |
1
plato.stanford.edu/entries/logic-games (and jelly not jam)
– Not Mike
Dec 5 '18 at 7:44
1
1
plato.stanford.edu/entries/logic-games (and jelly not jam)
– Not Mike
Dec 5 '18 at 7:44
plato.stanford.edu/entries/logic-games (and jelly not jam)
– Not Mike
Dec 5 '18 at 7:44
add a comment |
1 Answer
1
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oldest
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Yes, there is definitely a lot of interaction here. Once we move beyond first-order logic, semantics in general becomes very set-theoretic. So while studying game semantics for weak systems need not involve set theory, beyond a certain point we're arguably part of set theory. Vaanaanen's paper "Games and Trees in Infinitary Logic: A Survey" might be a good place to start; the epic volume "Model-theoretic logics" edited by Barwise and Feferman also has a great deal of information on the topic (and really everything else relating to logics beyond first-order), especially the chapter on game quantification (noting in passing that AD itself is essentially just De Morgan's law for the game quantifier, for countable structures).
answered Dec 5 '18 at 19:38
Noah SchweberNoah Schweber
122k10148284
add a comment |
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1 Answer
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active
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votes
Yes, there is definitely a lot of interaction here. Once we move beyond first-order logic, semantics in general becomes very set-theoretic. So while studying game semantics for weak systems need not involve set theory, beyond a certain point we're arguably part of set theory. Vaanaanen's paper "Games and Trees in Infinitary Logic: A Survey" might be a good place to start; the epic volume "Model-theoretic logics" edited by Barwise and Feferman also has a great deal of information on the topic (and really everything else relating to logics beyond first-order), especially the chapter on game quantification (noting in passing that AD itself is essentially just De Morgan's law for the game quantifier, for countable structures).
answered Dec 5 '18 at 19:38
Noah SchweberNoah Schweber
122k10148284
add a comment |
Yes, there is definitely a lot of interaction here. Once we move beyond first-order logic, semantics in general becomes very set-theoretic. So while studying game semantics for weak systems need not involve set theory, beyond a certain point we're arguably part of set theory. Vaanaanen's paper "Games and Trees in Infinitary Logic: A Survey" might be a good place to start; the epic volume "Model-theoretic logics" edited by Barwise and Feferman also has a great deal of information on the topic (and really everything else relating to logics beyond first-order), especially the chapter on game quantification (noting in passing that AD itself is essentially just De Morgan's law for the game quantifier, for countable structures).
answered Dec 5 '18 at 19:38
Noah SchweberNoah Schweber
122k10148284
add a comment |
Yes, there is definitely a lot of interaction here. Once we move beyond first-order logic, semantics in general becomes very set-theoretic. So while studying game semantics for weak systems need not involve set theory, beyond a certain point we're arguably part of set theory. Vaanaanen's paper "Games and Trees in Infinitary Logic: A Survey" might be a good place to start; the epic volume "Model-theoretic logics" edited by Barwise and Feferman also has a great deal of information on the topic (and really everything else relating to logics beyond first-order), especially the chapter on game quantification (noting in passing that AD itself is essentially just De Morgan's law for the game quantifier, for countable structures).
answered Dec 5 '18 at 19:38
Noah SchweberNoah Schweber
122k10148284
Yes, there is definitely a lot of interaction here. Once we move beyond first-order logic, semantics in general becomes very set-theoretic. So while studying game semantics for weak systems need not involve set theory, beyond a certain point we're arguably part of set theory. Vaanaanen's paper "Games and Trees in Infinitary Logic: A Survey" might be a good place to start; the epic volume "Model-theoretic logics" edited by Barwise and Feferman also has a great deal of information on the topic (and really everything else relating to logics beyond first-order), especially the chapter on game quantification (noting in passing that AD itself is essentially just De Morgan's law for the game quantifier, for countable structures).
answered Dec 5 '18 at 19:38
Noah SchweberNoah Schweber
122k10148284
answered Dec 5 '18 at 19:38
Noah SchweberNoah Schweber
122k10148284
answered Dec 5 '18 at 19:38
Noah SchweberNoah Schweber
122k10148284
answered Dec 5 '18 at 19:38
Noah SchweberNoah Schweber
122k10148284
122k10148284
add a comment |
add a comment |
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1
plato.stanford.edu/entries/logic-games (and jelly not jam)
– Not Mike
Dec 5 '18 at 7:44