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Logic on Math StackExchange
- Proving theorems in Hilbert/Ackermann formal system April 24, 2025I am working upon excersizes from "Introduction to Mathematical Logic" by Mendelson chapter 1.6. Given a formal system L1 : ∨ and ¬ are the primitive connectives. We use B -> C as an abbreviation for ¬B ∨ C. We have four axiom schemas: (1) B ∨ B -> B (2) B -> B ∨ […]user4035
- Implication versus conjunction [duplicate] April 24, 2025So I was going through the Rosen's book on Discrete Mathematics and I stumbled upon an example which had me confused from hours. This was the question: Consider these statements, of which the first three are premises and the fourth is a valid conclusion. i)“All hummingbirds are richly colored.” ii)“No large birds live on honey.” […]Ajay
- Do we have a term to describe all cases of a statement? April 24, 2025So a statement can be either true or false, and this is simple. But a statement itself can be a complex composite object in that it can be defined recursively, or, by many atomic statements, etc. In computer programming, we have "Boolean satisfiability problem", or, simply "SAT" to find a set of combinations that makes […]linear_combinatori_probabi
- Show that if a language with at least one constant and ψ(x) a formula then thre're a finite number of terms with no variables then ⊢ V_(i=1)^nψ_(ti/x) April 23, 2025The exercise is for an assigment of first order logic, concretly about formal proofs and satisfaction, I've working on it for a long time but I fail to realease what I'm missing.It's also very different from what we've seen during class and that's a big part of why I want to solve it. It says: […]Bañó
- 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
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