Abstract
In this chapter basic constructions on sets are reviewed and the Schröder-Cantor-Bernstein theorem is proved. This theorem is applied when calculating the cardinality of the real line. The Axiom of Choice (AC) and Zorn’s Lemma (ZL) are presented with several applications in mathematics and in cardinal arithmetic. The theory of well-orders is developed, including transfinite induction and recursion; the equivalence between AC, ZL and the Well-order theorem is rigorously proved.
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Moerdijk, I., van Oosten, J. (2018). Sets. In: Sets, Models and Proofs. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-92414-4_1
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DOI: https://doi.org/10.1007/978-3-319-92414-4_1
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