Ordinal Level

An example of an Ordinal Level notification.

The Ordinal Level is a minor Achievement-like feature with no clear production benefits. Your Ordinal Level increases when you first reach certain benchmark Ordinals, mainly used to show progression in the game.

When you achieve a record Ordinal Level, a banner notification is shown at the top right corner, informing you that you have reached a record Ordinal Level.

List of Benchmark Ordinals

Ordinal Level	Ordinal Required	Notes
1	0	The start.
2	ω	Minimum requirement to Maximize after Maximize.
3	ω2
4	ω3	Not possible in Base 3.
5	ω4	Not possible in Base 3 or 4.
6	ω2	Minimum requirement to Markup (result of Maximisation).
7	ω22	FS1 requirement (Ordinal).
8	ω3	FS2 requirement (Ordinal).
9	ω4	FS3 requirement (Ordinal).
10	ω10	Only possible in Challenge 3 and Challenge 7 due to their base limiting
11	ωω
12	ωω2
13	ωω+1
14	ωω+12
15	ωω+2	FS5 requirement (Ordinal).
16	ωω+3	Not possible in Base 3.
17	ωω2
18	ωω2+1	FS6 requirement (Ordinal).
19	ωω3	Not possible in Base 3.
20	ωω2	FS7 requirement (Ordinal).
21	ωω2+ω2
22	ωω2+1
23	ωω2+ω
24	ωω22
25	ωω23	From here to Ordinal Level 50, it can only be possible if the Base is 4 or higher. If at Base 3, OLs 25 to 50 are free.
26	ωω3	Base 4, 5, or 6.
27	ωω32	Base 4 or 5.
28	ωω4	Base 5 only.
29	ωω5	Although it would be ωω5, this can't be reached (665 = 67776 > 10270)
30	ωωω	Possible in Challenge 3. The Achievement Impossible, or is it? links to this.
31	ωωω+ω2
32	ωωω+1
33	ωωω+ω
34	ωωω2	Again, like with level 29, this is impossible (4442 = 4512 > 10270)
51	ψ(Ω)	Equal to ε0.
67	ψ(Ωω)	1 click cycle after ε0.
68	ψ(Ωψ(Ω))	4 click cycles after ε0.
70	ψ(Ω2)	8 click cycles after ε0.
77	ψ(Ω2ω)	9 click cycles after ε0.
78	ψ(Ω2ψ(Ω2))	16 click cycles after ε0.
90	ψ(Ωω)	24 click cycles after ε0.
94	ψ(Ωω2)	25 click cycles after ε0.
95	ψ(Ωωω)	26 click cycles after ε0.
96	ψ(Ωψ(Ω))	28 click cycles after ε0.
97	ψ(Ωψ(Ωω))	52 click cycles after ε0.
98	ψ(Ωψ(Ωψ(Ω)))	56 click cycles after ε0.
100	ψ(ΩΩ)	FB1 post-Collapse requirement.
102	ψ(ΩΩω)	FS8 (FB1 pre-Collapse) requirement.
103	ψ(ΩΩψ(ΩΩ))
104	ψ(ΩΩ+1)	FB2 requirement.
105	ψ(ΩΩ+ω)
106	ψ(ΩΩ2)	FB4 requirement.
107	ψ(ΩΩω)
108	ψ(ΩΩψ(ΩΩ))
109	ψ(ΩΩψ(ΩΩψ(ΩΩ)))
110	ψ(ΩΩ2)	Ackermann Ordinal. FB7 requirement.
111	ψ(ΩΩ2+ω)
112	ψ(ΩΩ2+1)	FB8 requirement. Also C2x2 goal.
113	ψ(ΩΩ2+ω)
114	ψ(ΩΩ2+Ω)	FB10 requirement.
115	ψ(ΩΩ2+Ωω)
116	ψ(ΩΩ22)	Double Ackermann Ordinal. FB16 requirement.
117	ψ(ΩΩ2ω)
118	ψ(ΩΩ2ψ(ΩΩ2ω))
119	ψ(ΩΩ2ψ(ΩΩ2ψ(ΩΩψ(ΩΩψ(ΩΩ2+ψ(ΩΩ2+ψ(ΩΩ2+2...)))))))	This isn't made up - this really is OL119.
120	ψ(ΩΩω)	SVO (Small Veblen Ordinal) exactly. Interestingly, the transfinitary-Veblen hierarchy isn't mentioned outside this one level.
122	ψ(ΩΩω)	122-125 are intended to be different from the SVO, but due to floating point nonsense there is no difference.
124	ψ(ΩΩω)
125	ψ(ΩΩω)
150	BHO
151	ψ(εΩ2)	Need SL2. Also known as ψ(Ω2Ω+ψ1(Ω2Ω))
152	ψ(εΩ2ΩΩ2ω)	Need SL41. Also known as ψ(Ω2Ω+ψ1(Ω2Ω)ΩΩ2ω)
153	ψ(εΩ2ω)	Need SL86. Also known as ψ(Ω2Ω+ψ1(Ω2Ω+ψ1(Ω2Ω)ω))
154	ψ(εΩ2Ω2)	Need SL342. Also known as ψ(Ω2Ω+ψ1(Ω2Ω+ψ1(Ω2Ω+Ω2)))
155	ψ(εΩ2εΩ2ΩΩ22+Ω+2)	SL ~e1.21e12. Need to be in the Incrementyverse. Also known as ψ(Ω2Ω2)
156	Ω	First uncountable ordinal

Trivia

• This was added in v0.34.
• A lot of this page was made with a program to automatically generate the ordinal requirements for each Ordinal Level. The following is the programs raw output:

Automated Wiki Editing:
1: 0
2: ω
3: ω2
4: ω3
5: ω4
6: ω²
7: ω²2
8: ω³
9: ω⁴
10: ω^ω
11: ω^ω
12: ω^ω2
13: ω^ω+1
14: ω^ω+12
15: ω^ω+2
16: ω^ω+3
17: ω^ω2
18: ω^ω2+1
19: ω^ω3
20: ω^ω2
21: ω^ω2
22: ω^ω2+1
23: ω^ω2+ω
24: ω^ω22
25: ω^ω23
26: ω^ω3
27: ω^ω32
28: ω^ωω
29: Ω
30: ω^ωω
31: ω^ωω
32: ω^ωω+1
33: ω^ωω+ω
34: Ω
51: ψ(Ω)
67: ψ(Ωω)
68: ψ(Ωψ(Ω))
70: ψ(Ω²)
77: ψ(Ω²ω)
78: ψ(Ω²ψ(Ω²))
90: ψ(Ω^ω)
94: ψ(Ω^ω2)
95: ψ(Ω^ωω)
96: ψ(Ω^ψ(Ω))
97: ψ(Ω^ψ(Ωω))
98: ψ(Ω^ψ(Ωψ(Ω)))
100: ψ(Ω^Ω)
102: ψ(Ω^Ωω)
103: ψ(Ω^Ωψ(Ω^Ω))
104: ψ(Ω^Ω+1)
105: ψ(Ω^Ω+ω)
106: ψ(Ω^Ω2)
107: ψ(Ω^Ωω)
108: ψ(Ω^Ωψ(ΩΩ))
109: ψ(Ω^{Ωψ(ΩΩψ(ΩΩ))})
110: ψ(Ω^Ω2)
111: ψ(Ω^Ω2ω)
112: ψ(Ω^Ω2+1)
113: ψ(Ω^Ω2+ω)
114: ψ(Ω^Ω2+Ω)
115: ψ(Ω^Ω2+Ωω)
116: ψ(Ω^Ω22)
117: ψ(Ω^Ω2ω)
118: ψ(Ω^{Ω2ψ(ΩΩ2ω)})
119: ψ(Ω^{Ω2ψ(ΩΩ2ψ(ΩΩψ(ΩΩψ(ΩΩ2+ψ(ΩΩ2+ψ(ΩΩ2+2...))))))})
120: ψ(Ω^Ωω)
122: ψ(Ω^Ωω)
124: ψ(Ω^Ωω)
125: ψ(Ω^Ωω)
150: BHO
151: ψ(ε_Ω2)
152: ψ(ε_Ω2Ω^Ω2ω)
153: ψ(ε_Ω2^ω)
154: ψ(ε_Ω2^Ω2)
155: Ω