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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.

      2
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      115 views

      Sunflower lemma in a more general poset?

      The sunflower 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 $P_\lambda(\kappa)$ for $\kappa$ ...
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      votes
      0answers
      125 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
      141 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 "...
      6
      votes
      2answers
      332 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
      182 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 $Q$...
      0
      votes
      1answer
      62 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
      213 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
      128 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
      87 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 ...
      1
      vote
      0answers
      48 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
      103 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
      111 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 ...
      0
      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
      158 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 ...
      9
      votes
      0answers
      257 views

      Connection between Provability Logic (GL) and geometry?

      In Provability Logic (aka GL) we have The Beth definability theorem and De Jong-Sambin Fixed Point Theorem The former has a vague similarity to the implicit function theorem in that you can loosely ...

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