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Results tagged with lo.logic
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user 15713
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.
6
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2
answers
2k
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Are all countable, nonstandard models of arithmetic given by ultrapowers?
Countable models of PA fall into two categories: the standard one $(\omega, S)$ and the nonstandard ones (all the rest). The only way I've seen to construct a nonstandard model is through taking an u …
- 168
4
votes
2
answers
606
views
Is there Ramsey Theorem for infinitary tuples?
I'm wondering if there's any sort of Ramsey relation that allows for the tuples to be of arbitrary infinite size $\mu$? This $\mu$ is below some strongly compact cardinal, so I'm not worried about la …
- 168
2
votes
From elementary equivalence to isomorphism
First, you should note that the signature is determined by the structures and any two structures that are elementarily equivalent or isomorphic have to have the same signature.
For your question, I d …
- 168
1
vote
0
answers
210
views
Existence of $\lambda$-transitive linear orders for $\lambda \geq \aleph_0$
A linear order $(L, <)$ is $\lambda$-transitive iff any order-preserving bijection between sets of size $\lambda$ can be extended to an order automorphism of $L$.
For $\lambda < \aleph_0$, $2$-transi …
- 168
1
vote
Accepted
Type implication
For the first one, elements of your expanded language might be definable in the smaller language. As a very simple example, consider $T = Th((\omega, S)$, the theory of the natural numbers with the s …
- 168