Here are the final drafts of the “Group Process Papers.” Assessment details will be distributed in class. Great work, everyone!
Tag: final papers
Logic on Math StackExchange
- Is this characterization of paraconsistent logic $C_\omega$ right? April 28, 2025Priest characterization of $C_\omega$ can be found here. It says that: To obtain da Costa’s system $C_\omega$, instead of the positive fragment of classical logic, we start with positive intuitionist logic instead. $C_i$ systems for finite $i$ do not rule out $(A^n \land \land \neg A^n \land A^{n+1})$ from holding in a theory. By going […]Lost definition
- A Weakly 2-Random Set that is both Hyperimmune and Generalized Low April 28, 2025In a 2007 paper, Nies, Montalbán and Lewis build a weakly 2-random set that is not generalized low, hence separating weak 2-randomness from randomness. This is done by constructing a 1-random hyperimmune-free not-generalized-low set, which by properties of randomness implies that this set is weakly 2-random but not 2-random. In the same paper, they show […]Robly18
- Axiomatic system for propositional logic is an empty sequence, why? [closed] April 28, 2025I study physics as my main degree, but I am currently attending lectures on differential geometry. We started with logic and I have a question about propositional logic and axiomatic systems. The definition that we were given about axiomatic systems is: "An axiomatic system is a finite sequence of propositions or propositional schemes $a_1,a_2...a_N$ which […]imbAF
- Is it known whether Free Complete Heyting Algebras Exist? April 27, 2025I was reading the wikipedia page for heyting algebras, and it made the claim that "it is unknown whether free complete heyting algebras exist". It came unsourced, but by tracking the edit I was able to source the claim to page 34~35 of Stone Spaces by Johnstone, where he says something which I can see […]Glubs
- a property between compactness and non-compactness in logic April 27, 2025Background and motivation: Without specifying exactly what "a logic" is (since any one definition would be unnecessarily restrictive for the purposes of this question), we can say that a logic is compact if it satisfies the analogue of the compactness theorem for FOL, that is, if a set of sentences is finitely satisfiable, then the […]Carlyle
- Are $1$, $2$, $3$... the only definable natural numbers? April 27, 2025Of course $1$, $2$, $3$... etc have defining axioms. If we're working with an $\omega$-inconsistent theory we can also have a natural number $m$ satisfying $\neg P(m)$ even though $P(1)$, $P(2)$, $P(3)$... etc are all provable. But we don't have uniqueness, so we can't add a defining axiom. Can there ever be a definable natural […]Pineapple Fish
- Is quantum mechanics complete -mathematically - [closed] April 26, 2025I have a question If we consider gödel's incompleteness theorems, then quantum mechanics mathematical formalism isn't coherent nor complete, then why did the Copenhagen interpretation scientists say that the mathematical foundation of quantum mechanics is no subject of objection ? "Nous tenons la mécanique des quanta pour une théorie complète, dont les hypothèses fondamentales, physiques […]Mohammed ramy Cherif
- In Velleman’s How to Prove It Example 1.1.2 (1), should “Either John went to the store, or we’re out of eggs” be modelled using exclusive OR? [duplicate] April 26, 2025I’m working through Daniel Velleman’s textbook How to Prove It: A Structured Approach (second edition). In Example 1.1.2 (1). The book analyses the statement: Either John went to the store, or we’re out of eggs. It models this as: $$P \lor Q$$ where: P = “John went to the store” Q = “We’re out of […]georgeamccarthy
- Does this Weird Correspondence of $\Box$ to $\top \to$ to the S4 Axioms Allow for a Companion to IS4 with No Modal Operators? April 26, 2025This just struck me as weird while I was reading a bunch of papers on modal decision procedures for intuitionistic propositional logic: N : If $A$ is a theorem, derive $\Box A$. ~ If $A$ is a theorem, derive $\top \to A$. K : $\Box (A \to B) \to (\Box A \to \Box B)$ ~ […]Joshua Harwood
- Help walking through difficulties understanding the difference between $\forall x$ and infinite conjunction April 26, 2025I (and possibly others) naively thought of $\forall$ as an infinite conjunction (only vaguely aware of others saying to avoid this interpretation of the $\forall$ sign). Years later I'm confronting this belief. I've read over Derek Elkins' blog post on the matter. I only partially probably have the logical prerequisites to approach the problem, but […]Pineapple Fish
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