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Questions tagged [lo.logic]

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.

3,315 questions
75 views

Order types of models of theories of ordinals

For $C$ a set of ordinals, let $\mathcal{L}(C)$ be the language with identity, a relation symbol for less than, function symbols for successor, addition, multiplication, and exponentiation, and a ...
23 views

80 views

Sentential, first order and higher logics from a categorical perspective

Is there a standard reference for understanding sentential, first and higher order logics from a categorical perspective? I'm close to knowing enough $1$/$2$/internal category theory to tackle the ...
180 views

Good texts (other than Kunen and Jech) on set theory, specifically on consistency proofs (reflection theorems, absoluteness, etc) [closed]

I'm finding Kunen and Jech bit of a hard read, and cannot seem to find good alternatives. Please suggest.
2k views

Defining the standard model of PA so that a space alien could understand

First, some context. In one of the comments to an answer to the recent question Why not adopt the constructibility axiom V=L? I was directed to some papers of Nik Weaver at this link, on ...
302 views

Turing independent refinement

Suppose $\kappa< 2^{\aleph_0}$ and $\langle P_i : i < \kappa\rangle$ is a sequence of perfect subsets of $2^{\omega}$. Can we find $Q_i \subseteq P_i$ for $i < \kappa$ such that each $Q_i$ is ...
443 views

Is categoricity retained when reducing the language?

Suppose $\mathcal L \subseteq \mathcal L’$ are first-order languages, $\kappa$ is a cardinal, and $T’$ is a theory in $\mathcal L’$ that is $\kappa$-categorical. Let $T = T’ \restriction \mathcal L$. ...
2k views

Status of proof by contradiction and excluded middle throughout the history of mathematics?

Occasionally I see the claim, that mathematics was constructive before the rise of formal logic and set theory. I'd like to understand the history better. When did proofs by contradiction or by ...
187 views

Generic saturation of inner models

Say that an inner model $M$ of $V$ is generically saturated if for every forcing notion $\Bbb P\in M$, either there is an $M$-generic for $\Bbb P$ in $V$, or forcing with $\Bbb P$ over $V$ collapses ...

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