MATH33011.pdf

# MATH33011.pdf - MATH33011 Two hours UNIVERSITY OF...

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MATH33011 Two hours UNIVERSITY OF MANCHESTER MATHEMATICAL LOGIC 18 January 2017 09.45 – 11.45 Answer ALL questions in Section A (56 marks in total). Answer TWO of the THREE questions in Section B (44 marks in total). If more than TWO questions from Section B are attempted, then credit will be given for the best TWO answers. The use of electronic calculators is not permitted. 1 of 3 P.T.O.

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MATH33011 SECTION A Answer ALL questions in section A. A1. (i) State the definition of a partially ordered set and of a well ordered set . Give examples of well orders 1 and 2 on the set N such that ( N , 1 ) and ( N , 2 ) are not isomorphic. No justification is required. (ii) State the definition of an ordinal and show that for each ordinal α , the set α * = α ∪ { α } is again an ordinal. (iii) State the definition of the cardinality of a set X and the definition of a cardinal . Show that there is no largest cardinal by applying and stating a result from the lectures.
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• Winter '17
• Math, Logic, Order theory, Natural number, Model theory, Total order

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