Hi everyone,

The grades for Exam #3 are posted under Dashboard / OpenLab Gradebook – the exams will be returned on Tuesday. Let me know if you have any questions.

Regards,

Prof. Reitz

Skip to the content

Hi everyone,

The grades for Exam #3 are posted under Dashboard / OpenLab Gradebook – the exams will be returned on Tuesday. Let me know if you have any questions.

Regards,

Prof. Reitz

- OpenLab #1: Advice from the Past – 2019 Fall – MAT 2071 Proofs and Logic – Reitz on OpenLab #7: Advice for the Future
- Franklin Ajisogun on OpenLab #7: Advice for the Future
- Franklin Ajisogun on OpenLab #3: “Sentences”
- Franklin Ajisogun on OpenLab #6: Proof Journal
- Jessie Coriolan on OpenLab #7: Advice for the Future

- Inaccessible cardinals and consistency of ZFC May 18, 2024I don't see how to state and prove rigorously the following result. Which of the following statement makes sense and is true ? For all $\phi$ in $ZFC$, we have : $ZFC+\exists \kappa'(\kappa' inaccessible)\vdash \forall\kappa(\kappa inaccessible\rightarrow \phi^{V_{\kappa}})$ For all $\phi$ in ZFC and for all inaccessible cardinal $\kappa$, we have : $ZFC+\exists \kappa'(\kappa' inaccessible)\vdash \phi^{V_{\kappa}}$ […]Mamoun Aich
- Can we build multiple models of PA within one the same model of ZFC? May 18, 2024Just to check my understanding I have the following (possibly dumb) question: can we build multiple models of PA (one standard and multiple non-standard) within one same model of ZFC?user341
- Clarification on model satisfaction definition and satisfaction over classes May 18, 2024By the completeness theorem of logic, we have "A theorem $T$ is consistent if and only if it has a model $M$" - whereby $M$ is a model of $T$ if and only if all the non-logical axioms of $T$ are valid in $M$. Now, suppose that $M$ is a model of $T$, and $\phi$ […]Link L
- Graphs of recursive functions May 18, 2024Recently I've been studying the relationship between recursiveness of a function and recursiveness of its graph (i.e. recursiveness of the characteristic function of the graph). First, we have Theorem 1: If $f:\mathbb{N}\to\mathbb{N}$ is primitive recursive, then its graph is primitive recursive. The converse is false, as witnessed by the Ackermann function for example. In an […]blargoner
- Why can't we derive the Left Contraction Rule in predicate logic? May 17, 2024Suppose we only have all the standard left and right logical inference rules ($∧L_{1}$, $∧L_{2}$, $∨L$, $→L$, $¬L$, $∨R_{1}$, $∨R_{2}$, $∧R$, $→R$, $¬R$) and on top of that 4 quantifer rules (see the Wikipedia page: https://en.wikipedia.org/wiki/Sequent_calculus) My professor said that in predicate logic we cannot prove the Left Contraction Rule unlike in Propositional logic (without […]Alessandra12342
- Models of ZFC and inaccessible cardinals May 17, 2024For a homework I have to show that working in $ZFC$, we have $(ZC)^{V_{\lambda}}$ for all limit ordinal $\lambda>\omega$. Now in my lecture notes the relativization is defined for a class $C$ characterized by a formula $\psi_C(x)$ (i.e. $x\in C$ if and only if $\psi_C(x)$ holds) as follows : $(\forall x\phi)^C:=\forall x(\psi_C(x)\rightarrow \phi^{C})$ and $(\exists […]Mamoun Aich
- Languages with quantification over *formulas*? May 17, 2024The 4th page of this paper mentions: A first-order language that contains “substitutional quantifiers” (with formulas as substituends) in addition to ordinary quantifiers turns out to be precisely the sort of “infinitary” language that we need So, it seems to be describing a sort of extension of first-order logic where you can quantify over formulas […]NikS
- Clarification on "absolute" property May 17, 2024I read that if some property $P(x)$ defined by a formula $\phi$ is absolute for some class $M$, then $\phi(P(x)) \leftrightarrow \phi^M(P(x))$, where $\phi(P(x))$ is interpreted in $V$, and $\phi^M(P(x))$ is relativized to $M$, which is a subclass of $V$. In most texts in set theory (i.e. proof that $R$ (axiom of regularity) is consistent […]Link L
- Godel's Second Incompleteness Theorem on $L$ May 17, 2024Am an absolute beginner here. But I've read that if a sentence $A$ is a theorem of a Theory $T$, then $T[\neg A]$ is inconsistent (where $T[\neg A]$ means that $\neg A$ is added as a logical axiom to $T$. Now, if say some axiom $A$ were shown to be not provable in $ZF$ then […]Link L
- Confusion on Section 1.2 of Rosen's Discrete Math Textbook May 16, 2024So I was able to deduce based on the rule that p implies q is the same as q unless (not p) that this is same as: (not s) -> (r -> (not q)) I could use the logical equivalence (A -> B) = (A or (not B)) to get Rosen's result, but up to […]Bob Marley

"Math Improve"
.999
1
assignment
assignments
calculus
calendar
Doodling
exam #3
exam 3 grades
final papers
grading criteria
grading policy
graph theory
group paper
group project
homework
logic
mathography
metacognition
only if
openlab
OpenLab #4: Bridges and Walking Tours
OpenLab7
OpenLab 8
OpenLab8
Open Lab 8
openlab assignment
perfect circle
points
presentation
project
resource
rubric
semester project
spring classes
vi hart
ViHart
visual math
Wau
webwork
week 8
week 14
welcome
written work

© 2024 2018 Fall – MAT 2071 Proofs and Logic – Reitz

Theme by Anders Noren — Up ↑

Our goal is to make the OpenLab accessible for all users.

top

Our goal is to make the OpenLab accessible for all users.

## Leave a Reply