# David Toth

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bio website www1.maths.leeds.ac.uk/~mmdt location age member for 2 years, 7 months seen 6 hours ago profile views 164

2010 - 2014, Imperial College London, MEng Computing (Artificial Intelligence)

2014 - 2017, University of Leeds, a PhD candidate in Computability Theory

# 257 Actions

 Dec13 asked Motivation behind automorphism bases? Dec12 revised Notation for the class of all cardinals added 8 characters in body Dec12 accepted Notation for the class of all cardinals Dec12 asked Notation for the class of all cardinals Dec8 awarded Caucus Dec5 answered Recursion theory text, alternative to Soare Dec4 awarded Benefactor Dec2 comment If $P$ a probability of a sentence to be true, then $\{P(\phi | T_i)\}_{i \in \mathbb{N}}$ is a martingale over constructed theories $T_i$ @MauroALLEGRANZA Thank you for your answer, sorry I did not reply to your comment earlier, I needed to understand more, as given in your answer. Dec2 comment If $P$ a probability of a sentence to be true, then $\{P(\phi | T_i)\}_{i \in \mathbb{N}}$ is a martingale over constructed theories $T_i$ @Stef See Mauro's reply that clarifies in the end why $\emptyset$ is treated as a tautology. Dec2 accepted If $P$ a probability of a sentence to be true, then $\{P(\phi | T_i)\}_{i \in \mathbb{N}}$ is a martingale over constructed theories $T_i$ Nov30 awarded Promoter Nov28 comment If $P$ a probability of a sentence to be true, then $\{P(\phi | T_i)\}_{i \in \mathbb{N}}$ is a martingale over constructed theories $T_i$ @Ilya Could they use a different definition of a martingale? Let $\phi$ be a non-trivial sentence, i.e. that is not true and not false. Then let $T_1=\{\phi\}$. Then $X_0=P(\phi)\neq 1$, but $X_1=P(\phi|\{\phi\})=1$. As $X_0 \neq X_1$, this sequence extensible to a martingale cannot be constant. Nov28 comment If $P$ a probability of a sentence to be true, then $\{P(\phi | T_i)\}_{i \in \mathbb{N}}$ is a martingale over constructed theories $T_i$ @Ilya Yes, the sequence has deterministic values. What is a constant sequence? The sequence above does not have all the values the same for every $i \in \mathbb{N}$ in general. Yes, $P$ is defined on the sentences, that is the abuse of notation. Nov28 asked If $P$ a probability of a sentence to be true, then $\{P(\phi | T_i)\}_{i \in \mathbb{N}}$ is a martingale over constructed theories $T_i$ Nov22 comment $\exists G \in L'. G \iff \mathtt{True}(gn(\neg G))$ in the language $L'$ with Godel numbering $gn$ and $\mathtt{True}$ predicate? @MauroALLEGRANZA Thanks, hence what I want to prove seems to follow from the diagonal lemma. Nov22 asked $\exists G \in L'. G \iff \mathtt{True}(gn(\neg G))$ in the language $L'$ with Godel numbering $gn$ and $\mathtt{True}$ predicate? Nov19 accepted What is effectively continuous? Nov17 answered What is effectively continuous? Nov17 awarded Popular Question Nov17 asked What is effectively continuous?