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- Set System of Indeterminates [closed] January 12, 2026I've made a "meta-mathematical" system that attempts to describe Indeterminates in mathematics, I've been going around and resolving contradictions and updating the Axioms, but my knowledge and experience and limited so I'm asking for your help in eliminating them. Article 1 Article 2 both of these are stored on github, in markdown (.md) format, the […]FlytoTheSpace
- Truth tables meaning when statements are specific [duplicate] January 12, 2026I just need some clarification re truth tables P -> Q is true if P is false and Q is true. That is usual. BUT If I now assign P to be the statement "f is differentiable" and Q to be "f is continuous" I am led to the conclusion that "f is not differentiable […]Mathman
- First-Order Formula with Finitely Many Satisfying Assignments January 10, 2026This question came up in research in formal verification. Let $\phi(x)$ be a universal first-order logic formula, such that for any structure $s=(D,I)$ we have only finitely many elements $d\in D$ such that $s,[x\mapsto d]\models\phi(x)$. I want to show that it must be the case that $\phi$ may only be satisfied by closed terms. That […]Raz Lotan
- Why is LTL straightforwardly expressible in S1S? January 10, 2026I was thinking about the question in the title and I reached the following conclusions: S1S (monadic second-order logic of one successor) is interpreted over $(\mathbb{N},S)$, where $S(x,y)$ means $y=x+1$. An LTL model is an infinite word $w=w_0 w_1 w_2\ldots$, so time points correspond exactly to natural numbers. Each atomic proposition $p$ of LTL is […]user1868607
- Under what circumstances can $\textrm{ZFC}$ fail to prove a theorem for a 2-adic isometry $f^{-1}$ but not for $f$? [closed] January 10, 2026Let $a,b$ be a pair of odd natural numbers. Let $f$ be a member of the isometry group of the 2-adic field $\Bbb Q_2$ and let $f$ satisfy $f(2x)=2f(x)$. $(1)$ Let $f$ topologically conjugate $x\mapsto a_1x+b_1$ to $x\mapsto a_2x+b_2$ over $\Bbb Z_2^\times\to \Bbb Z_2$ and fix $f(0)=0$. Or if you prefer, a semantically equivalent statement […]Robert Frost
- Why is or isn't this Collatz Conjecture scenario logically consistent with ZFC? What mathematical conclusion does this lead us to? [closed] January 9, 2026Suppose that there exists a semantic counterexample $X$ against to the Collatz Conjecture in the standard natural numbers, which diverges to the infinity, so does not lead to the any cyclic loop and ZFC can not prove or disprove $X$ is an actual counterexample, which means proving that $X$ is an actual counterexample is independent […]Noah
- What is the class of "set-inductive" predicates? January 8, 2026I don't know enough about formal set theory to be able to state this rigorously, but I think the question itself is meaningful. Alice claims that if a property holds for each of an increasing (in the sense of inclusion) sequence of sets, then the property must also hold for the limit (union). Bob points […]Jack M
- Does assumption after universal instantiation cause errors in a proof? January 8, 2026I was working with a proof in Velleman's book “How to prove it?” I came across this problem where it asks to seek if the proof is right or wrong, Theorem? Suppose $A$, $B$, and $C$ are sets and $A⊆B∪C$. Then either $A⊆B$ or $A⊆C$. Is the following proof correct? If so, what proof strategies […]Dipanjan Das
- Foundations of mathematics for an undergraduate [closed] January 7, 2026I'm a fourth year undergraduate that plans to work in index theory, so I'm not interested in professionally understanding foundations, mathematical logic, set theory, etc. Can you recommend some concise books or lecture notes on foundations that explain basic concepts? I don't have much time to go in depth, I just would like to have […]andrey safin
- Is the union of a chain of structures elementary in a union of a chain of elementary extensions? January 7, 2026There is a problem I'm working on and I'm having trouble knowing if a simple fact is true or false. I've been looking at this for some time and I don't seem to be able to prove it or find a counter example. For a fixed first order language, consider two chains of structures $M_0\subseteq […]Susana Santoyo
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