Generalized Löb's Theorem. Strong Reflection Principles and Large Cardinal Axioms. Consistency Results in Topology and Homotopy Theory. J. Foukzon Israel Institute of Technology, Haifa, Israel jaykovfoukzon@list.ru Abstract. In this article we proved so‐called strong reflection principles corresponding to formal theories which has ‐models. An possible generalization of the Löb's theorem is considered. Main results are: (1) let be an inaccessible cardinal and is a set of all sets having hereditary size less , (2) there is a Lindelöf ₃ indestructible space of pseudo then , then character ₁ and size ₂ in . Keywords: Löb's theorem, second incompleteness Gödel theorem, consistency, formal system, uniform reflection principles, ‐model of , standard model of ,inaccessible cardinal, weakly compact cardinal, Lindelöf space. MSC:03E55,54A25 References [1] J.Foukzon, GeneralizeLöb'sTheorem. http://arxiv.org/abs/1301.5340 [2] J.Foukzon, An posible generalization of the Löb's theorem. AMS Sectional Meeting AMS Special Session.Spring Western Sectional Meeting University of Colorado Boulder, Boulder, CO April 13‐14, 2013. Meeting #1089 http://www.ams.org/meetings/sectional/2208_program_saturday.html [3] F.D. Tall, On the cardinality of Lindelöf spaces with points G_{δ}, Topology and its Applications 63 (1995), 21‐38. [4] ] J.Foukzon, Consistency Results in Topology and Homotopy Theory, Pure and Applied Mathematics Journal. Special Issue: Modern Combinatorial Set Theory and Large Cardinal Properties. Vol. 4, No. 1‐1, 2015, pp. 1‐5. doi: 10.11648/j.pamj.s.2015040101.11