Week 2 Assignments
Written work – none
WeBWorK – Assignment #1 and #2, due Tuesday, September 6th, at midnight.
OpenLab – OpenLab #2, due Thursday, September 8th, at the start of class.
Handy Links
Recent Comments
Logic on Math StackExchange
- Why get an invalid conclusion from the tautology when premise is true? August 16, 2024The formula is a tautology: (p →(q ∨ r)) → ((p →q)∨(p →r)) The simple proof: p → p p → q = ¬ p V q p →(q ∨ r) = ¬ p V q V r (p →q)∨(p →r) = (¬ p V q) ∨(p →r) = (¬ p V q) ∨ (¬ […]showkey
- Smallest natural number unrepresentable by fifty letters August 16, 2024What is the problem of the proof of this claim? I also think it is really strange, but I can't find the problem. Claim: All natural numbers can be uniquely represented using fifty letters. Proof: Assume that claim is wrong. Let $X \subseteq \mathbb{N}$ which contains all natural numbers that can not be uniquely represented […]이상원
- Are these two statements the same statement under the given constraints? August 15, 2024This question is a follow-up of this other question, which I posted a few months ago and which received a valid answer. I will now re-state the original question, and will add the new information at the end. Let $A$ and $B$ be arbitrary finite sets, and let $f:A\to B$ be a function with domain […]EoDmnFOr3q
- Algorithm for fixed point in provability logic August 15, 2024I am studying Boolos "the logic of provability" and cannot follow the procedure on page 110 it gives an algorithm for finding fixed points in "modalized p-sentences" (sentences where the variable p only appears within the scope of a box.) But how to get the fixed point of for example []([]p-> -[]-p) $$ \square \left( […]Whogius
- Did Jim Carrey get away with lying in 'Liar Liar'? [closed] August 14, 2024In the movie 'Liar Liar', on a particular day Jim Carrey cannot tell a lie. But I believe that he did make a false statement that day. In the 'The pen is blue' scene he threatened his hand (@1:50 here: https://www.youtube.com/watch?v=dAE7uOO_4v4), "Write it or I'll break it off." A few seconds later, he writes 'blue' […]Mr. Bobbins
- I am learning about non-well-founded sets and I wanted to know what books everyone recommends. August 14, 2024I am currently studying "A Course in Model Theory" by Bruno Poizat and I am doing research with altering the set of set theory's axioms. I want to further learn about the effect of the axiom of regularity and non-well-founded sets. I have already had someone recommend Peter Aczel's "Non-Well-Founded Sets" and I was curious […]Jackson Willoughby
- Modal logic: condition corresponding to $\Diamond \Box (A \Rightarrow B)\Rightarrow (\Diamond \Box A \Rightarrow \Diamond \Box B)$? August 14, 2024In normal modal logic, what would be the condition on the accessibility relation corresponding to the following axiom (the analogue of the distribution axiom for $\Diamond \Box$ instead of $\Box$): $\Diamond \Box (A \Rightarrow B)\Rightarrow (\Diamond \Box A \Rightarrow \Diamond \Box B)$? I know that this schema is derivable in S5 and S4.2, but not […]mtphil
- If $\Gamma$ is consistent, then $\rho(\Gamma)$ ($\Gamma$ with only even constants) is consistent. August 14, 2024Let $L$ be a formal language. Let $\Gamma$ be a set of formulas of $L$. Let also $\rho: \{c_i\} \to \{c_i\}$ be a function defined by $\rho(c_i) = c_{2i}$. That is, a function which takes each constant to an even constant. Extend the definition of $\rho$ to terms and formulas in the most obvious manner […]Promethèus
- Metalanguage & Metatheory in FoST August 13, 2024I would like to ask for literature recommendations on foundations of set theory focusing on the treatment of the concepts & the nature of metalanguage & metatheory, so the language&theory used to reason about the object theory. Especially, to what extent can one treat it or parts of it with formal rigor as in the […]user267839
- Are closed formulas and propositions the same? [duplicate] August 13, 2024$x=1$ is not a proposition because if $x$ is zero it is false and if $x$ is one it is true. Such a formula is called an open formula. Then, are all closed formulas—formulas without free variables—propositions? I think that $\forall x \in \mathbb{R} (x=1)$ is a proposition, because it has a truth value False. […]BBB
Leave a Reply