You can find them on the “Grades” page (email me if you don’t remember the password).
The exams will be returned on Tuesday.
Best,
Prof. Reitz
Logic on Math StackExchange
- What is the proof that Term Finding in Calculus of Constructions ($\lambda{C}$) is undecidable? May 9, 2024It is mentioned in a textbook "Type Theory and Formal Proof: An Introduction", but couldn't find the paper or proof anywhere on the internet. To quote the textbook: The question of Term Finding, however, is decidable in $\lambda{\rightarrow}$ and $\lambda\underline{\omega}$, but undecidable in all other systems. It goes on to cite the "Church–Turing Undecidability Theorem" […]Vivek Joshy
- How completeness fails in second order logic [duplicate] May 9, 2024Gödel's completeness theorem proves that in first order logic, if a theory is consistent (we cannot derive a contradiction), then it has a model. As discussed in this question, there are theories which are consistent but do not have a model. In particular, the completeness theorem does not apply to second order logic. I would […]Weier
- Question about the meaning of logical implication [duplicate] May 8, 2024So, I came across the following equivalence: $$(p \to q) \equiv (\neg p \lor q)$$ Which I had been knowing for a while, but I never quite understood. I understand when it's used this way: I assert $p \land (p\to q)$, it follows that $q$. In other words, asserting $p \to q$ is like saying […]Elvis
- At most A does not occur May 8, 2024Let $A$ and $B$ be two events in the sample space $S$. Describe & represent the following event in terms of $A$ and $B$: "at most $A$ does not occur". This is a question that someone asked me, and I think it is meaningless as "at most" makes no sense here. Am I right? Or […]Fermat
- On the limitations(?) of first-order logic in mathematical reasoning May 8, 2024Note: This is a follow-up to this earlier question. Also, for the purpose of this question, I'll use the term "normal mathematics" to refer to topics other than "foundational" ones like logic and set theory. On the one hand, it seems like only a relatively small minority of "normal mathematics" is explicitly written out in […]NikS
- Is there a constructive proof of the 4 axiom in $\sf Grz$? May 7, 2024Willem Blok managed to prove that the 4 axiom of modal logic $\Box \phi \to \Box \Box \phi$ is provable in $K+ \Box (\Box(\phi \to \Box \phi) \to \phi) \to \phi$. Let $\psi=(\phi \land (\Box \phi \to \Box \Box \phi))$. Blok managed to prove 4 by using the theorem of system $K$ $\Box (\phi \to […]PW_246
- What does it mean to "suppose" a proposition in proofs? May 7, 2024I have been putting some thought lately to proofs by contradiction and have the following question. When proving theorems we usually use the word "Suppose P(x)" where P is a proposition, but what do we mean by "suppose"? All propositions are either T or F, and, under some interpretation, their truth value is fixed. Hence, […]Agustin G.
- Why can't we prove CL rule (structural rule) in predicate logic (with quantifiers) [closed] May 7, 2024My professor said that the following rule rule is proven in propositional logic but not in predicate logic? Is there an explanation to that?Alessandra12342
- Proving that Union of finite set with finite elements is finite without Axiom of Choice May 7, 2024How can I without using any form of the axiom of choice, prove that if the set $A$ is finite and all its elements are finite, then the set $\bigcup A$ is also finite? This is the only task that I didn’t do in my homework :( ,so I would really appreciate your help.Maria S.
- if the sequents (Γ ⊢ ψ) and (∆ ⊢ ψ) are both correct, then so is the sequent ((Γ ∩ ∆) ⊢ ψ) May 7, 2024This comes from Chriswell mathematical logic. It is not so clear to me. It's stating that if ψ is provable from assumptions in Γ and also from assumptions in ∆, it is provable from the intersection of the assumptions in Γ and ∆. But since there can be different proofs of a statement it could […]nskywalker
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