[1]Arens, R., The adjoint of a bilinear operation,
Proc. Amer. Math. Soc., 2 (1951), 839-848.
[2]Bell, J. L., Fremlin, D. H.,
A geometric form of the axiom of choice,
Fund. Math., 77 (1972), 167-170.
[3]Cartan, H.,
Filtres et ultrafiltres,
C. R. Acad. Sci. Paris, 205 (1937), 777-779.
[4]Chang, C. C., Keisler, H. J.,
Model Theory, 3rd. ed.,
North-Holland Publishing Co., Amsterdam, 1990 .
[5]Dales, H. G.,Banach Algebras and Automatic Continuity,
Clarendon Press, Oxford, 2000.
[6]Daws, M.,
Ultrapowers of Banach algebras and modules,
Glasg. Math. J., 50 (2008), 539-555.
[7]Dineen, S., Complete holomorphic vector fields on the second dual of a Banach space,
Math. Scand., 59 (1986), 131-142.
[8]Faal, R., The Second Dual of the Algebra of Bounded Operators and Tensor Products,
Master`s thesis, Ferdowsi University of Mashhad, 2013.
[9]Faal, R., Ebrahimi Vishki, H. R., More on the Arens regularity of B(X),
Bull. Austral. Math. Soc., 94 (2016), 296-303.
[10]Faal, R., Ebrahimi Vishki, H. R., Dean’s identity and the principal of local reflexivity,
[11]Godefroy, G., Iochum, B., Arens-regularity of Banach algebras and the geometry of Banach spaces
J. Funct. Anal., 80 (1988), 47–59.
[12]Goldblatt, R., Lectures on the Hyperreals; an Introduction to Nonstandard Analysis, Springer-
Verlag, Graduate Texts in Mathematics, vol.188, Springer-Verlag, Berlin, 1998.
[13]Hamilton, A. G., Logic for Mathematicians, Cambridge University Press, Cambridge, 1988
[14]Harlpern,J. D., Levy, A., The Boolean prime ideal theorem does not imply the axiom of choice,
axiomatic set theory part 1, Proc. Symp. Pure Math., 13 (1971), 83–134.
[16]Hindman, N., Strauss, D., Algebra in the Stone-Cech Compactification- Theory and Applications,
Walter de Gruyter, Berlin, 2012.
[17]Iochum, B., Loupias, G., Remarks on the bidual of Banach algebra (the C* case), Annales scientifiques
de l’Universitй de Clermont-Ferrand, sйrie Mathйmatiques, 27 (1991), 107-118.
[18]Iochum, B., Loupias, G., Arens regularity and local reflexivity principle for Banach algebras,
Math. Ann., 284 (1989), 23–40.
[19]Jech, T. J., The Axiom of Choice, Dover Books on Mathematics, Dover, New York, 2008.
[20]Kirman, A., Sondermann, D., Arrow’s theorem, many agents, and invisible dictators, J. Econ.
Theory, 5 (1972), 267–277.
[21]Khosravi, A. A., Ebrahimi Vishki, H. R., Peralta, M., Aron-Berner extensions of triple maps with
applications to the bidual of Jordan Banach triple system.
[22]Łoś, J., Ryll-Nardzewski, C., On the application of Tychonoff’s theorem in mathematical proofs,
Studia Math., 38 (1951) 233–237.
[23]Luxemburg, W. A. J., Two applications of the method of construction by ultrapowers to analysis,
Bull. Amer. Math. Soc., 68 (1962), 416–419.
[24]Luxemburg, W. A. J., Reduced powers of the real number system and equivalents of the Hahn-
Banach extension theorem, in Appl. Model Theory Algebra, Anal., Probab., Proc. Int. Sympos.
Calif. Inst. Technol., 1969, 123–137.
[25]Martínez-Abejón, A., An elementary proof of the principle of local reflexivity, Proc. Amer. Math.
Soc., 127 (1999), 1397–1398.
[26]Pincus, D., Independence of the prime ideal theorem from the Hahn Banach theorem, Bull. Amer.
Math. Soc., 78 (1972), 766–770.
[27]Pincus, D., The strength of the Hahn-Banach theorem, Lecture Notes in Mathematics, vol. 369,
Springer-Verlag, Berlin, 1974, 203–248.
[28]Tao, T., Hilbert’s Fifth Problem and Related Topics, American Mathematical Society, Providence
RI, 2014.
[29]Vaught, L. R., Alfred Tarski’s work in model theory J. Symbolic Logic, 51 (1986), 869–882.
[30]Wang, H.,A logical Journey: From Godel to Philosophy,
Bradford Book, Massachusetts, 1977.
)