Here are the final drafts of the “Group Process Papers.” Assessment details will be distributed in class. Great work, everyone!

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### Logic on Math StackExchange

- Example of a family of Boolean subalgebras such that their union is not a Boolean algebra February 26, 2024I read that given a family of Boolean subalgebras, their union is not in general a Boolean algebra except if the family is directed. What is an example of a family of Boolean subalgebras whose union is not a Boolean algebra?Link L
- How to resolve nested if then statements resulting from using the conditional identity. February 25, 2024If I want to turn the "p or q" part of an "if p or q then r" statement into an if then statement using the conditional identity then how do I resolve the nested if then statement that results from that. It seems like it would literally become if if p then q then […]Sam Spencer
- Forcing with the generic multiverse February 25, 2024Fix a countable transitive model $M$ and consider the collection $\mathbb{P}$ of all forcing extensions of $M$ (i.e., the generic multiverse of $M$), ordered by reverse containment. What happens if we force with the partial order $\mathbb{P}$? Does it collapse $\omega_1$ or $\mathfrak{c}$? Is it equivalent to $\mathrm{Col}(\omega,\omega_1)$ or some other well-known poset? What kind […]Lxm
- In logic, how can "safe" mean "ground?" February 25, 2024I'm working through an [automated reasoning paper]1. Thy make a statement (shown here in bold) that I can't figure out on page 9: The hypertableau calculus (Baumgartner et al., 1996) is based on the observation that,if the literals in $C_1σ\lor...\lor C_n σ$ do not share variables, we can replace the clause with a nondeterministically chosen […]Cort Ammon
- Understanding Peirce's law February 25, 2024I am trying to understand the meaning of Peirce's Law, namely: [(P→Q)→P]→P What does this mean? I am trying to find a practical example of P and Q where the truth of P would follow from the truth of P→Q. Any suggestion?Bilou
- Is "yesterday it was sunny" a proposition? February 25, 2024I'm studying logical proposition. And I know that $P$ is a proposition if it's either true (T) or false (F), there are no other possibilities than being (T) or (F) and it can't be true and false. I know for exemple that "tomorrow it will be sunny" is not a proposition, because we can't know […]joshua
- The Error-Correction Procedure calculation in AI? February 25, 2024I have the following homework (AI-related) with solution: There is a training set is in the form of (s1, ..., s8, d), where the first 8 elements are the Pacman’s sensor readings, and d is the label of this input, with d = 1 meaning a positive, and 0 a negative example. Now ,I need […]oscar
- Is the Axiom of Completeness logically equivalent to "There is no proper superset of $\mathbb R$ that is an ordered Archimedean field"? February 25, 2024The Axiom of Completeness can be formulated as: There exists a set $R$ such that: $R$ is an ordered Archimedean field Any nonempty subset of $R$ with an upper bound has a least upper bound. Recently, I read something that suggested this is logically equivalent to the following: There exists a set $R$ such that: […]SRobertJames
- Property Equivalent to Maximally Consistent February 24, 2024This is a question about Gentzen calculus. $X$ is a set of formulas with the symbols $\{\lnot, \land\}$, and $a$ is such a formula. On page 27 of "A Concise Introduction to Mathematical Logic" by Rautenberg, it states: it easily follows that $X$ is maximally consistent iff either $a \in X$ or $\lnot a \in […]Enrico Borba
- When mathematicians say "true" do they mean "true in all models"? February 24, 2024According to the comments to this question, Truth is ordinarily defined by reference to models. If so, even axioms and theorems are not true without reference to a model. However, when mathematicians say "this is true," they are usually not referring to a specific model. Is he saying "true in all models"?MathMan

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