Mathematical Logic: Lecture 4
Last time: Turing computability and uncomputability
Today: Abacus computability and recursive functions
The concept of abacus machines
All abacus computable functions are Turing computable
All recursive functions are abacus c

Mathematical Logic: Lecture 8
Today: Syntax and semantics of rst-order logic
Assignment 3
Part 1: Ex9.6, Ex9.7, Ex10.11, Ex10.14
Due in 3 weeks
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Syntax and semantics
Throughout our treatment of formal logic, it is important to
dis

Mathematical Logic: Lecture 3
Today: Turing computability and uncomputability
The concept of Turing machines
The concept of Turing computability, i.e., a function is
computable by a Turing machine
Examples of Turing uncomputable functions: the halting
fun

Mathematical Logic: Lecture 6
Last time: Recursive functions and recursive relations
Today: Equivalent denitions of computability
All Turing-computable functions are recursive (8.1)
Corollaries of the equivalence of the three denitions of
computability (8

Mathematical Logic: Lecture 7
Last time:
Equivalence of three denitions of computability
Important corollaries
Today: Semirecursive relations (7.2)
and recursively enumerable sets (8.3)
Mathematical Logic
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Review of last time
Theorem. All Turing com

Mathematical Logic: Lecture 5
Last time: Abacus computability and recursive functions
All abacus computable functions are Turing computable
All recursive functions are abacus computable
Today: Recursive functions and recursive relations
Recursive function

Mathematical Logic: Lecture 2
Today: distinguish between two kinds of innite sets, the
enumerable and the nonenumerable (q8q8)
The concepts
Examples of enumerable sets
Examples of nonenumerable sets (the diagonal argument)
Assignment 1
Part 1: Ex 1.6, Ex