Do the Two Operations Addition and Multiplication Commute with Each Other?

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References

[1] Zermelo-Fraenkel Set Theory—Wikipedia, the Free Encyclopedia.

[2] Abian, A. (1965) The Theory of Sets and Transfinite Arithmetic. W B Saunders.

[3] Abian, A. and LaMacchia, S. (1978) On the Consistency and Independence of Some Set-Theoretical Axioms. Notre Dame Journal of Formal Logic, 19, 155-158.

http://dx.doi.org/10.1305/ndjfl/1093888220

[4] Devlin, K. (1984) The Joy of Sets. Springer.

[5] Fraenkel, A., Bar-Hillel, Y. and Levy, A. (1958) Foundations of Set Theory. Fraenkel’s Final Word on ZF and ZFC, North Holland.

[6] Hatcher, W. (1968) The Logical Foundations of Mathematics. Pergamon.

[7] Jech, T. (2003) Set Theory: The Third Millennium Edition, Revised and Expanded. Springer.

[8] Kunen, K. (1980) Set Theory: An Introduction to Independence Proofs. Elsevier.

[9] Montague, R. (1961) “Semantic Closure and Non-Finite Axiomatizability” in Infinistic Methods. Pergamon, London, 45-69.

[10] Suppes, P. (1960) Axiomatic Set Theory. Dover Reprint. Perhaps the Best Exposition of ZFC before the Independence of AC and the Continuum Hypothesis, and the Emergence of Large Cardinals. Includes Many Theorems.

[11] Takeuti, G. and Zaring, W.M. (1971) Introduction to Axiomatic Set Theory. Springer Verlag.

[12] Tarski, A. (1939) On Well-Ordered Subsets of Any Set. Fundamenta Mathematicae, 32, 176-183.

[13] Tiles, M. (1989) The Philosophy of Set Theory. Dover Reprint. Weak on Metatheory; the Author Is Not a Mathematician.

[14] Tourlakis, G. (2003) Lectures in Logic and Set Theory. Vol. 2, Cambridge University Press, Cambridge.

[15] van Heijenoort, J. (1967) From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press. Includes Annotated English Translations of the Classic Articles by Zermelo, Fraenkel, and Skolem Bearing on ZFC.

[16] Zermelo, E. (1908) Untersuchungen uber die Grundlagen der Mengenlehre I. Mathematische Annalen, 65, 261-281.

http://dx.doi.org/10.1007/BF01449999

[17] van Heijenoort, J. (1967) Investigations in the Foundations of Set Theory. From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. Source Books in the History of the Sciences, Harvard University Press, 199-215.

[18] Zermelo, E. (1930) Uber Grenzzablen und Mengenbereiche. Fundamenta Mathematicae, 16, 29-47.