# TU Wien:Advanced Mathematical Logic VU (Fokina)

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## Daten

Lecturers Ekaterina Fokina 3 Advanced Mathematical Logic (en) summer semester 2021SS "if required in english" was not recognized as a supported language code. tiss:104394

## Inhalt

2021S: Structures and Theories, Completeness, Compactness, Back-and-Forth and Quantifier elimination, Gödel's Incompleteness Theorem, Computable and Decidable Structures.

2021S: It starts with definitions of terms, formulas, structures/interpretations, first-order theories. There is some algebra stuff as example but also a lot of new notions (representability, Gödel's incompleteness, quantifier elimination, compactness) that should count as continuation of that "pure logic start" and not math.

## Ablauf

2021S: A few recorded zoom lectures, two exercise sheets. Oral exam by appointment at the end.

## Benötigte/Empfehlenswerte Vorkenntnisse

2021S: For computer science bachelor definitely the Discrete Mathematics course. Topics like rings and fields are examples in the script. Also topics like transfinite cardinals are relevant.

2021S: The proof tutorial from formal methods in computer science might be a nice refresher. You need to proof a lot.

2021S: Doing Computability Theory course by Prof Fokina prior helps with some notions like computable, computably enumerable, and halting set.

## Vortrag

2021S: Professor Fokina gave an overview of the most important topics in the script.

## Übungen

2021S: Two exercise sheets with some proofs. She corrected my exercise sheets during my exam at the end of summer, so I guess accomodating late hand in might have been possible.

## Prüfung, Benotung

2021S: You can write the professor an email whenever you feel ready. Exam is oral. Two tasks:

1. Proof of a theorem in the script (not something that takes a whole page, but not a one-liner either) and also relevant defintions and an example of where you can use the definition.
2. "Unrelated" to the script. Build a computable structure such that some relation is and some other relation is not computable. It was necessary to know halting set K, that it is computably enumerable but not computable, computable structures, isomorphism.

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## Unterlagen

Script as PDf that contains everything.

## Tipps

Use the internet. StackExchange/MathOverflow helps really much.

Following the references in the script also yielded one or the other solution.

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