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Results tagged with lo.logic
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user 20343
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
2
votes
1
answer
370
views
Uniqueness of super godel numbers of $\varphi$ and $\neg \varphi$
Let $e_{0},e_{1},...,e_{n}$ be a sequence of wffs or other expressions. Code each $e_{i}$ by a regular godel number $g_{i}$, to yield a sequence of numbers $g_{0},g_{1},...,g_{n}$. Then encode this se …
- 1,441
0
votes
What is the metamathematical interpretation of knot diagrams?
It seems that you may trust algebra more as a solid foundation for how to describe a mathematical object, so you may be interested in the classification of knot diagrams by knot polynomials, such as t …
5
votes
1
answer
580
views
Completeness of a Theory from the Categorical Viewpoint
I am interested in a more specific reference or explanation of "the categorical view" explained in the article http://ncatlab.org/nlab/show/theory#CategoricalView. In particular, I am interested in tr …
- 1,441
0
votes
Accepted
On the Combinatorial Classification of Modal Kripke Frames
I happened to end up writing a paper which answered my question if anyone else is ever interested in this topic or comes across this question:
"On Generalizing a Temporal Formalism for Game Theory to …
- 1,441
2
votes
2
answers
267
views
Adjoint of Pushout as Modal Operators in Internal Logic
Regarding the internalization of mathematics to a particular category as in the nLab article: Internal Logic, there is a peculiar table mentioned in the section on Categorical Semantics in which there …
- 1,441
2
votes
2
answers
281
views
On the Combinatorial Classification of Modal Kripke Frames
We have that S5 modal logic is characterized by the modal axioms $K$, $M$ (reflexive), $4$ (transitive), and $B$ (symmetric). That is, an equivalence relation on a set of possible world (which can be …
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5
votes
2
answers
2k
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How many models of Peano arithmetic are isomorphic to the standard model and how many models...
I am currently writing a paper on non-standard models of Peano arithmetic and I am having trouble finding references or information that discuss the relative sizes of how many models of Peano arithmet …
- 1,441
7
votes
4
answers
904
views
Reference Request: Non-Standard Models of PA
I am attempting to write an expository paper on non-standard models of PA that is accesible to students taking an introductory graduate course in mathematical logic (covering Godel's incompleteness th …
- 1,441
7
votes
1
answer
443
views
Under what conditions does $\mathcal{M} \vDash \mathsf{PA}$ and $\mathcal{K} \vDash \mathsf{...
I'm currently learning some introductory model theory from Marker's "Model Theory: An Introduction", Kaye's "Models of Peano Arithmetic", and Hodges' "Model Theory", and I am confused by the Wikipedia …
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16
votes
4
answers
4k
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How are Modal Logic and Graph Theory related?
I am currently taking a graduate logic course on Modal Logic and I can't help notice that there are a certain class of graphs characterized by the modal axioms such as (4) $\Box p \rightarrow \Box \Bo …
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