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• We study a frustrated general spin-S Ising antiferromagnet on a kagome lattice. • We explore possibility of long-range ordering for any finite or infinite values of S. • Character of the spin-correlation function is studied by Monte Carlo simulations. • It is found that system remains disordered for any spin S and any finite temperature. The possibility of the emergence of some kind of long-range ordering (LRO) due to the increase of multiplicity of the local degrees of freedom (spin value S) is studied in an Ising antiferromagnet on a kagome lattice (IAKL) by Monte Carlo simulation. In particular, the critical exponent of the spin correlation function, obtained from a finite-size scaling analysis, is evaluated for various values of S , including S = ∞ , with the goal to determine whether there exists some threshold value of the spin S C above which the system would show true or quasi-LRO, similar to a related model on a triangular lattice (IATL). It is found that, unlike in the IATL case, the IAKL model remains disordered for any spin value and any finite temperature. [ABSTRACT FROM AUTHOR]