Week 2 Assignments
Written work – Sec 1.8 p.28: 3, 5, 6, 8, Due Tuesday, September 12th, at the start of class.
NOTE: On this assignment, odd problems are worth 3 points, even problems worth 5 points.
WeBWorK – Assignment #2, due Tuesday, September 12th, at midnight.
OpenLab – OpenLab #2, due Thursday, September 14th, at the start of class.
Logic on Math StackExchange
- Proof of countable Borel uniformization December 14, 2024Corollary 13.8 of these notes says that the Borel sets are closed under Borel functions whose fibers are all countable. Trying to digest that proof, but there's a step I'm unable to follow. I'll recap the proof and then point to what I'm not getting. For $f: Z \to X$ Borel function with all fibers […]user1510061
- bijection between n and k letter alphabet [closed] December 13, 2024What is bijection between strings over n and k letter alphabet, k,n positive integers ? I'm about to construct a bijection for sentences and binary strings, but I've failed . Can I construct a bijection such that length of the sentence in MSL is non-decreasing ? Can I characterize all the bijections ?Jan Pax
- Generalization (semantic) proof for Hilbert-Calculus December 12, 2024I constructed this lean proof to the Generalization Rule in the Hilbert System. I have marked the passage where I am not sure if I overdo. It may not be proper language but I want it to be better readable for me in the future. Theorem: Let $\Sigma$ be an axiom system of the Hilbert […]God
- Propositional logic: Finding the maximum length of an implication chain December 12, 2024Particular definitions, Let $\mathcal{L}$ be a language of a propositional logic. For each sentence $\psi$ in $\mathcal{L}$, denote by $T_{\psi}$ the set of all truth assignments $\mathfrak{U}: \mathcal{L} \rightarrow \{$true, false$\} $ s.t $\psi^{\mathfrak{U}}$ is true. A sequence $\langle \psi_0, \dots, \psi_{l-1} \rangle$ of sentences in $\mathcal{L}$ is said to be an implication chain of […]Pexx
- How to construct a propositional logic formula to enforce a certain relation? December 11, 2024Disclaimer: this is a question from a homework but i am really struggling with it and would like to get some help. I have a set of students $S$, set of Time-slots $T$,set of cookies $P$ and the relation $M \subseteq (S\times P)$ where each tuple means that the student likes that cookie type. now […]fady abo swees
- What is wrong with my Prenex normal form? [closed] December 11, 2024I had this equation $$∃yG(y)→¬(∀xF(x,y)↔G(y)).$$ Then I turned it to $$∀y(¬G(y)) \lor ∀x(F(x,y))\land ¬G(y) \lor ∃x(¬F(x,y))\land G(y).$$ Then I turned it to Prenex normal form: $$∀k∀s∃m(¬G(k) \lor F(s,y)\land ¬G(y) \lor ¬F(m,y)\land G(y)).$$ My professor says that something is wrong with my last equation. She said that I used too many quantifiers and changed the meaning […]Пчеловод
- The definition of inconsistency in a logical theory December 11, 2024A classical definition of inconsistency is the theory leads to contradictory statements Shoenfield: Mathematical Logic defines this on page 42 that A theory T is inconsistent if every formula of T is a theorem of T I guess this is because in classical logic there's the ex falso quodlibet rule, from false implies everything, which […]Gergely
- Unsure about soundness of proof about transitivity. December 11, 2024sorry in advance for any imprecision, missing tags etc but this is my first question. I'm reading Daniel J. Velleman 'How To Prove It' and i'm having a hard time understanding how to write a sound proof. I encountered an exercise that i think can help me understand a lot and since there is no […]Luca
- Would solving the Liar's Paradox allow for self-meta-logics? December 11, 2024By self-meta-logic, I mean a logic that is its own meta-logic; a logic that can talk abouts its models. If I understand correctly, this is impossible (for "interesting" logics at least) due to Tarski's Undefinability Theorem. Any "interesting" logic will derive this theorem, which means that if that logic contains a truth predicate, it would […]user110391
- Is there a "tree of derivations" construction? December 10, 2024My question stems from the following observation: in Logic we construct a series of finitary syntactical structures by means of trees. First we have the base constants, variables, and function symbols, from which we make terms through chains (i.e. trees). From there we construct formulas as trees whose nodes are our previously constructed terms + […]Sho
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