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Results tagged with lo.logic
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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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BL Algebras that allow for Compactness to hold
Say we have a model $M$ of a theory $T$ of some core fuzzy logic.
When dealing with compactness, we run in to a situation where the new model being built (by the use of compactness over $M$), will ne …
- 185
2
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answers
129
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Kripke semantics for fuzzy logics
I am interested in Fuzzy logic.
I have a problem about Gödel Logic, I'm studying Kripke semantics for fuzzy logics and have found the necessary and sufficient conditions on Kripke frames for satisfyin …
- 137
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112
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"The" axiom of induction up to recursive ordinal $\alpha$ in $\mbox{PRA}$
As far as I understand, Kriesel proved that there exists a recursive relation $R$ of order type $\omega$ such that $\mbox{PRA}+TI(R)$ proves $\mbox{Con}(PA)$, and Beklemishev proved that for any recur …
- 1,307
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206
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What are proofs of the consistency of the propositional calculus?
Consider the propositional calculus. For specificity I will use the sequent propositional calculus PK as developed in Cook and Nguyen's Logical Foundations of Proof Complexity (for precision the axiom …
- 1,974
3
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138
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Is every union-closed family of set the set of solutions of some co-HORNSAT formula?
Related to the Union-closed sets conjecture.
Let $\phi$ be a co-HORNSAT
on variables $x_1 \ldots x_n$ in CNF format.
This means in every close at most one literal is negative.
The solutions of $\phi …
- 25.4k
2
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0
answers
123
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Consistency of bounded finitely axiomatized set theories [closed]
If $T$ is a consistent first order finitely axiomatized set theory having an axiom that defines V and the rest of axioms are all of the form:
$\forall x1 ..xn \in V \exists x \in V \forall y \in V ( …
- 11.3k
1
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0
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252
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A compact notation for conditional set operations [closed]
I'm trying to write down the definition of the type-3 grammar in pure mathematics and there is a rule $S \rightarrow \epsilon$ which can be in the ruleset under a certain condition. I've come up with …
- 11
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260
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Are there two mutually incompatible consistent sentences in the language of PA, neither of w... [closed]
Are there sentences $\phi$ and $\psi$ in the language of PA and models $\mathcal{M}_\phi$ and $\mathcal{M}_\psi$ of PA such that $\mathcal{M}_\phi\models\phi$ and $\mathcal{M}_\psi\models\psi$, but $\ …
- 151
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139
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All decidable predicates have corresponding statements in a formal language? [closed]
My book states the following theorem with no proof. Can anyone give an outline of the proof, or an explanation of how the formal statement is to be constructed?
Theorem:
Suppose that $M(x_1,...,x_n) …
- 111
2
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159
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About Tarski's axioms A and A' (2): transitive sets
2-By A'2, every set y satisfying axiom A' must be a transitive set. But it is not true that every set y satisfying axiom A must be transitive. So, it seems natural to ask the following.
Question 2: (i …
- 2,655
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195
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About Tarski's axioms A and A' (3): 16 equivalent axioms
3-On the same page (84) he states axioms A and A', Tarski also considers the 16 following axioms variants for A and A' and asserts witout giving a proof that they are all equivalent.
Axiom C: "For ev …
- 2,655
2
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291
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About Tarski's axioms A and A' (4): ZFC + Tarski-Grothendieck axiom
4-(suite): axiom A (or equivalently axiom TG) have powerfull consequences.
(i) It is easy to see that A1 and A2 prove the power-set axiom, by separation, because P(x is included inside the set y;
(ii) …
- 2,655
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365
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Ultraconsistency & Truth
Let $D$ be an effectively generated set of recursive ordinals that contains $0$ and that is closed under an effectively defined ordinal successor function "$+1$" and that have a well defined relation …
- 11.3k
2
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184
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Is the existence of undecidable propositions decidable?
In proving his first incompleteness theorem Godel constructed a proposition that is undecidable, i.e. neither provable nor disprovable within a consistent formal system $F$ that contains elementary ar …
- 4,862
1
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0
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65
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Algebraization of arithmetic and stronger theories?
Intuitionistic and classical propositional logic, and even classical first-order logic with identity, have algebraic counterparts. Algebraizable logics, 1989, by Willem J. Blok and Don Pigozzi, is a c …
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