Tag: .999
Logic on Math StackExchange
- Forcing to add a Kurepa tree with many branches April 22, 2025$\newcommand{\dom}{\operatorname{dom}}$$\newcommand{\ran}{\operatorname{ran}}$A Kurepa tree is a tree with height $\omega_1$ that has countable levels and at least $\omega_2$ branches. There is a standard $\sigma$-closed forcing that adds a Kurepa tree; see e.g. Example 6.1 in Cummings' handbook chapter; there he focuses on inaccessible cardinals but the same definition works for successors. Here is a natural variant […]Fanxin Wu
- Does literal-polarity-based assignment have a theoretical basis in SAT solving? April 21, 2025I'm exploring a heuristic idea for assigning truth values in 3-SAT instances based on how often each variable appears as a positive or negative literal. I’ve tested it on small random instances (e.g. 100 variables and 400 clauses), and it seems to work surprisingly well — but I don’t know if it’s meaningful from a […]Portes N
- Prove that the following formula is a theorem in natural deduction April 21, 2025Prove that the formulaRanko
- what is the fuzz about Nelson-grelling paradox all about? [duplicate] April 20, 2025A predicate is a first order formula with one free variable. Working in the standard structure of the natural numbers Let $A(x)$ be an arbitrary predicate the formula $A(“A(x)”)$ is false iff $“A(x)”$ codes a heterological predicate (1): IF for all predicates $x$ , $A(x)$ iff $x$ codes a heterological predicate , THEN $A(“A(x)”)$ iff […]Logician Meta
- Godel’s Dichotomy solution??? [closed] April 19, 2025Either mathematics is incompletable in this sense, that its evident axioms can never be comprised in a finite rule, that is to say, the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable diophantine problems of the type specified. If f=0 […]Lawrence Wickert
- Equivalence of these two statements April 18, 2025I was working with limit definitions and have been wondering why these two statements are equivalent:Jonathan Cellucci
- First order logic: What does it mean to prove a sentence? April 15, 2025I understand that in "normal" proofs such that the one used in linear algebra, if you find a counter example to a statement, then that statement is false (or is not always true). And for all things that satisfies the premises of the statement, the conclusion of the statement is also true. Is this also […]Incömplete
- Under what circumstances that one Skolem function can be used to substitute another? [closed] April 15, 2025in the context of first order logic, and in the process of resolution refutation, under what circumstances that I can make a substitution $g(x) | h(y)$? where both $g$ and $h$ are Skolem functions. The obvious case is that $f = g$ and $x$ unifies with $y$, but how can I know that $f = […]Incömplete
- The word "Necessary" in Logic! [duplicate] April 15, 2025Consider the sentence "Robert needs to start working at 5 am to finish the deck by 6 pm.". If we let p: "Robert starts work at 5 am" and q: "Robert finished the deck by 6 pm", does the above sentence indicate $p\to q$ or $q\to p$? I am thinking $p\to q$, but does the […]Chesso
- Could AC show that a "missing" set exists? (countable model) (follow-up) April 15, 2025This is a follow-up to "https://math.stackexchange.com/questions/5055976/could-replacement-show-that-a-missing-set-exists-countable-model". The powerset P(N) contains all pairs of naturals "that exist". This is all of the pairs because of the axiom of pairing applied to each pair. However in a countable model there are many (most) sets of naturals that "don't exist". In P(N), could we first use separation to […]Dave Selke
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