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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.

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        423 views

        Does “every” first-order theory have a finitely axiomatizable conservative extension?

        I originally asked this question on math.stackexchange.com here. There's a famous theorem (due to Montague) that states that if $\sf ZFC$ is consistent then it cannot be finitely axiomatized. ...
        5
        votes
        0answers
        191 views

        Sunflower / $\Delta$-system lemma in a more general poset?

        The sunflower lemma (or $\Delta$-system lemma) may be viewed as a statement about the poset $P_\omega(\omega_1)$, and the generalized sunflower lemma may be viewed as a statement about the poset $P_\...
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        votes
        0answers
        190 views

        Can we get rid of the primitive symbol $V$ in Ackermann's set theory this way?

        I want to get rid of the primitive $V$ in Ackmerann set theory, without changing the axioms so much. I have the following try in my mind, but I'm not sure if it works. So we instead work in the pure ...
        4
        votes
        0answers
        153 views

        Ultrapower of a field is purely transcendental

        Let $F$ be a field, $I$ a set, and $U$ an ultrafilter on $I$. Is the ultrapower $\prod_U F$ a purely transcendental field extension of $F$? According to Chapter VII, Exercise 3.6 from Barnes, Mack "...
        8
        votes
        2answers
        372 views

        Constructivist defininition of linear subspaces of $\mathbb{Q}^n$?

        Let me preface this by saying I'm not someone who has every studied mathematical logic or philosophy of math, so I may be mangling terminology here (and the title is a little tongue in cheek). I (and ...
        3
        votes
        1answer
        200 views

        Models of $\mathsf{ZFC}$ with neither $P$- nor $Q$-points

        A $P$-point is an ultrafilter $\scr U$on $\omega$ such that for every function $f:\omega\to\omega$ there is $x\in {\scr U}$ such that the restriction $f|_x$ is either constant, or finite-to-one. A $Q$...
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        votes
        1answer
        64 views

        Quantifier elimination and where is this quantified convex program in the polynomial hierarchy?

        I have a quantified convex program of the form that I need to solve $$\exists(x_{1,1},\dots,x_{1,n})\in\mathbb R^n\quad\forall(x_{2,1},\dots,x_{2,n})\in\mathbb R^n$$ $$\vdots$$ $$\exists(x_{2t-1,1},\...
        2
        votes
        2answers
        217 views

        (Types of) induction on infinite chains

        This question may be trivial, or overly optimistic. I do not know (but I guess the latter...). I am a group theorist by trade, and the set-up I describe cropped up in something I want to prove. So ...
        11
        votes
        0answers
        149 views

        Ordinal-valued sheaves as internal ordinals

        Let $X$ be a topological space (feel free to add some separation axioms like “completely regular” if they help in answering the questions). Let $\alpha$ be an ordinal, identified as usual with $\{\...
        4
        votes
        0answers
        88 views

        Is Ackermann's set theory minus class comprehension equal to ZF?

        Ackermann in 1956 proposed an axiomatic set theory. Reinhard proved that Ackermann's set theory equals ZF It's clear that Zermelo set theory can be interpreted in Ackermann's set theory minus class ...
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        vote
        0answers
        50 views

        Is there a three valued logic whose game semantics corresponds to potentially infinite games?

        Consider game trees with the following properties: Each node in the tree is one of the following: Verifier Choice: Has one or more children Falsifier Choice: Has one or more children No Choice: Has ...
        2
        votes
        0answers
        107 views

        Definable modal logics in first-order structures

        Suppose $X$ is a set, $\mathcal{W}$ is a family of subsets of $X$, and $\mu:\mathcal{W}\rightarrow\mathcal{W}$ is an operation on those sets. There is a natural way to assign a modal logic to the ...
        5
        votes
        1answer
        115 views

        Amorphous proper classes in MK

        Working in $ZFC$ every cardinal is either finite or in bijection with a proper subset of itself (Dedekind infinite). Without Choice it is consistent that there are infinite sets which can't be ...
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        votes
        0answers
        32 views

        Combinatorial Logic for Rigid Logic

        It's straightforward enough to derive a combinatorial logic for linear and ordered logic, by just taking the standard translation for intuitionistic logic, and modify the lambda-application case to ...
        7
        votes
        2answers
        162 views

        Logic with “co-relations” - sources?

        My question is on a seemingly-natural extension of classical logic that I've been playing around with a bit in the context of generalized recursion theory. I'm sure it's been treated extensively ...

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