Tag: .999
Logic on Math StackExchange
- Does model theory in set theory require "arithmetization"? September 8, 2026Reading many set theory and model theory textbooks, it's clear that model theory is developed inside set theory, usually ZFC. My question is, does this necessarily require a form of arithmetization? To be clear, by arithmetization I mean not only coding logic symbols as integers, but also as sets more generally. In this sense, my […]conscontreras
- Math shorthand symbol for "assume" September 6, 2026I had a Discrete Methods professor years ago who used a very specific symbol for "assume" that I have never seen anywhere else. It was a capital "S" with a small vertical line through the bottom of it. She would write things like "[symbol] $\varphi$. We have that..." (where $\varphi$ is some formula). She used […]jorb
- Is there a proof of Kolmogorov's theorem using logic? September 3, 2026I believe there are many Kolmogorov theorems, I am referring to the extension one (see https://en.wikipedia.org/wiki/Kolmogorov_extension_theorem ). I encountered it in a course, and the statement feels very compactness-like (in the sense that we have a statement that says finite consistence entails consistence), so I wondered if there is a smart way of using standard […]Tarallino_Birichino
- What are some "everyday" examples of proof techniques? August 31, 2026I once had a teacher who, when introducing "Proof by contradiction", made the observation that although the formal structure could seem daunting on a first encounter, the following argument (in natural language) made sense to everyone: The murder took place in Los Angeles on Saturday, but my client was in New York the entire weekend. […]Robert Lee
- Axiom of choice in the proof that closed sets of Noetherian spaces are unions of finitely many irreducible subsets. [duplicate] August 31, 2026Hartshorne Proposition 1.5 states that any closed subset of a Noetherian topological space can be written as a union of finitely many closed irreducible subsets. A Noetherian topological space is a topological space that satisfies the descending chain condition on its closed subsets. I have one question regarding the proof of this theorem, and another […]khashayar
- Proof-technique for the Following Claim August 26, 2026I am trying to learn how to prove statements by studying proof techniques for common claims. Right now, I am wondering how to prove claims of the following form: Claim. Show that some subset $L$ of the universal set $U$ is the smallest set that contains all sets $S_{1}, \dots ,S_{m}$. For example, the claim […]MickeLil
- Law of excluded middle to show units of formal power series August 22, 2026Let $R$ be a commutative ring with unity, and $R[[x]]$ be the ring of formal power series of $R$. While I was reading Commutative ring theory by Matsumura, I saw that an element $$f=a_0+a_1x+a_2x^2+\cdots$$ is a unit iff $a_0$ is a unit. The discussion related to this somehow bothers me logically. Consider the following conversation […]khashayar
- Please recommend some books in Russian on mathematical logic for beginners. August 16, 2026I want to understand the proofs of Gödel’s incompleteness theorems, but I’m not familiar with mathematical logic or advanced mathematics. I also don’t know what mathematical induction is. I recently graduated from high school. Please recommend some books (or one book) on mathematical logic for beginners to help me get a grasp of the subject. […]Marmajuck
- Consistency of sets of modal literals under Horn constraints August 16, 2026Consider a multimodal logic with modalities of three types: $\mathsf{K}_A$, $[a]$, and $\mathbf{U}$ ($A\in\mathtt{Ag}$ — agents, $a\in\mathtt{Ac}$ — actions, $\mathtt{Ag}\cap\mathtt{Ac}=\varnothing$). In other words, we consider the logic $\mathbf{K}_m\oplus\mathbf{S5}_n$ with the universal modality. The semantics is given in terms of Kripke models $\mathfrak{M}=\langle W,\mathsf{R},\mathsf{E},V\rangle$ with $W\neq\varnothing$ (set of states), $\mathsf{R}=\langle R_a\rangle_{a\in\mathtt{Ac}}$ being a sequence of binary […]Daniil Kozhemiachenko
- When are parentheses actually needed in formulae in first-order logic? August 14, 2026Suppose $\mathcal L$ is a vocabulary consisting of function symbols and relation symbols of given arities (we regard constant symbols as function symbols of arity $0$). Recall that the set of $\mathcal L$-terms is the smallest set $T$ such that: Every variable is an element of $T$, If $f$ is an $n$-ary function symbol, and […]Joe
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