Hi everyone,

The Fall 2018 Calendar for this course has been updated – the final version is now available on the Calendar page.

Regards,

Prof. Reitz

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Hi everyone,

The Fall 2018 Calendar for this course has been updated – the final version is now available on the Calendar page.

Regards,

Prof. Reitz

- Clarification on logical equivalence, bi-conditionals, and operators May 21, 2024What are the differences between $$ vs $\iff$ vs $\equiv$ in terms of biconditionals and logical equivalence? Kindly please let me know :)Bob Marley
- Need some clarifications on Domain of Discourse in Quantified Statements May 21, 2024Screenshots from Rosen's discrete Math textbook. Here's how they define logical equivalence involving quantifiers: Statements involving predicates and quantifiers are logically equivalent if and only if they have the same truth value no matter which predicates are substituted into these statements and which domain of discourse is used for the variables in these propositional functions. […]Bob Marley
- Studying modal logic using category theory May 21, 2024When reading about modal logic, namely general frames and algebras, I've been seeing a lot of potential functors and/or universal properties. Like constructing an algebra with Boolean operators from a frame seems functorial, or canonical frames maybe having some universal property, etc. (not sure if any of this is true, it just seems like it […]tses
- Paper rejected twice, once because it proved two true statements imply each other, once because it proved two false statements imply each other? May 21, 2024I remember a while back finding an anecdote about a paper in set theory from the early 20th century establishing an equivalence between two concepts (I think, but I’m not sure, that it was the axiom of choice and the well-ordering principle). The story goes that the paper was rejected from one journal with the […]templatetypedef
- Is it circular to include reachability from $0$ like this as a Peano axiom? May 21, 2024I am wondering whether it makes logical and semantic sense to include, as an axiom to define the natural numbers, that "every natural number is either $0$ or the result of potentially repeated successor operations from $0$ ", where one idea I have to define what it means to be repeatedly use the successor operations […]Princess Mia
- Can a proper class be a member of a set? May 21, 2024From my understanding, the concept of a class was created to distinguish those objects describable using the language of set theory but ineligible to be a set due to potential contradictions. There exists a definition in NBG stating that a class can be considered a set if it belongs to another class, and it is […]Bezina Taki
- Does the axiom of induction hold iff every natural number is either $0$ or is the result of repeated successor operations on $0$? May 21, 2024I am wondering whether we could replace the axiom of Induction with an axiom saying that every natural number is either $0$ or can be expressed as repeated successor operations from $0$ (keeping all of the rest of the Peano Axioms), and get a logically equivalent set of axioms to the regular Peano axioms, in […]Princess Mia
- How much choice is needed for the Hat problem and how much is missing? [duplicate] May 20, 2024There is a 'well known' Problem in Math called the hat Problem where a countable infinite number of prisoners each get assigned a hat with colour red/blue and they have to guess their colour with only seeing the colours of everyone except their own. The Question is if there exists a strategy such that only […]Daniel Weichhart
- Specific example of a property $P$ that Peano arithmetic proves holds true for every specific number, but not for all numbers. May 20, 2024Can someone give a specific example, if there is any, of a predicate $P(x)$ expressible in the language of Peano arithmetic, such that the first-order theory of Peano Arithmetic proves $P(0)$, $P(1)$, $P(2)$, etc, but does not prove $(\forall x)P(x)$?user107952
- Confusion on using "unless" more than once in proposition May 20, 2024I'm having trouble interpreting this highlighted sentence (from Discrete Math Rosen Textbook) properly due to using unless more than once in this sentence. I understand that q unless (not p) is the same as saying p implies q, but I'm not sure how to exactly apply that rule here for this sentence. Is it equivalent […]Bob Marley

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